Proving  fixed point theorem in a fuzzy metric space is not possible for  Meir-Keeler contractive mapping. For this, we introduce the notion of $c_0$-triangular fuzzy metric space. This new space allows us to prove some fixed point theorems for  Meir-Keeler contractive mapping. As some pattern we introduce the class of $alphaDelta$-Meir-Keeler contractive and we establish some results of fixed ...

In this paper, we consider the eigenvalue problems for fourth order integral boundary value problems on time scales for an increasing homeomorphism and homomorphism with sign changing nonlinearities. By using a fixed point index theorem, we give the existence of eigenvalue intervals in which there exist one symmetric positive solution to the problem. An example is also given to demonstrate the ...

This paper is concerned with the one-dimensional p-Laplacian multi-point boundary value problem on time scales : (φp(u Δ))∇ + h(t)f(u) = 0, t ∈ [0, T ] , subject to multi-point boundary conditions u(0) −B0 m−2 i=1 aiu (ξi) = 0, u(T ) = 0, or u(0) = 0, u(T ) + B1 m−2 i=1 biu Δ(ξ′ i) = 0, where φp(u) is p-Laplacian operator, i.e., φp(u) = |u| u, p > 1, ξi, ξ′ i ∈ [0, T ] , m ≥ 3 and satisfy 0 ≤ ξ...

We use Krasnoselskii’s fixed point theorem to show that the nonlinear neutral differential equation with delay d dt [x(t)− ax(t− τ)] = r(t)x(t)− f(t, x(t− τ)) has a positive periodic solution. An example will be provided as an application to our theorems. AMS Subject Classifications: 34K20, 45J05, 45D05

Through the application of the upper-lower solutions method and the fixed point theorem on cone, under certain conditions, we obtain that there exist appropriate regions of parameters in which the fractional differential equation has at least one or no positive solution. In the end, an example is worked out to illustrate our main results. c ©2016 All rights reserved.

In this article, we consider nonlocal p-Laplacian boundary-value problems with integral boundary conditions and a non-negative real-valued boundary condition as a parameter. The main purpose is to study the existence, nonexistence and multiplicity of positive solutions as the boundary parameter varies. Moreover, we prove a sub-super solution theorem, using fixed point index theorems.

We study singular discrete nth order boundary value problems with mixed boundary conditions. We prove the existence of a positive solution by means of the lower and upper solutions method and the Brouwer fixed point theorem in conjunction with perturbation methods to approximate regular problems. AMS subject classification: 39A10, 34B16.

In this paper, the method of upper and lower solutions and the Schauder fixed point theorem are used to investigate the existence and uniqueness of a positive solution for a class of nonlinear fractional differential equations with non-monotone term. An example is also given to illuminate our results. 2000 MSC: 34B15 • 34B18

Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally convex topological vector space $E$ and $T:Krightarrow E$ is a continuous mapping, then there exi...

We use Krasnoselskii’s fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the neutral delay difference equation x(n+ 1) = a(n)x(n) + c∆x(n− τ) + g(n, x(n− τ)). AMS Subject Classifications: 39A10, 39A12.